Resumen de Construccion del "Soddy's Hexlet" por reducción a un caso trivial

Eugenio Roanes Macías , Eugenio Roanes Lozano

• Three spheres are given, two of them contained in the third one and each one tangent to the two other spheres. With this configuration, sequences of tangent spheres that are externally tangent to the first and second given spheres and internally tangent to the third one are to be found. Curiously, these sequences are finite, i. e., cyclic, consisting exactly of six spheres. Such a finite sequence is called a "Soddy's Hexlet".

  A constructive method to determine such a sequence, that reduces the general case to a trivial one and is original of the authors of this article, is presented. The corresponding algorithm is also detailed below. It has been implemented on a computer algebra system by the authors.